Problem: Find the smallest positive four-digit number that is divisible by each of the four smallest prime numbers.
Explanation: We want to find the smallest four-digit number that is a multiple of lcm[2, 3, 5, 7] = 210, so we need to find the smallest value of $n$ such that $$ 210n \ge 1000. $$Dividing this inequality by 210 we get $n \ge 4\, \frac{16}{21}$, so $n = 5$ gives us the smallest four-digit multiple of 210: $210 \cdot 5 = \boxed{1050}$.